算法：BFS宽度优先遍历

本篇总结的是BFS算法，BFS算法相比起DFS算法来说还是比较简单的

BFS与Queue相结合

N叉树的层序遍历

/*
// Definition for a Node.
class Node {
public:
    int val;
    vector<Node*> children;

    Node() {}

    Node(int _val) {
        val = _val;
    }

    Node(int _val, vector<Node*> _children) {
        val = _val;
        children = _children;
    }
};
*/

class Solution 
{
public:
    vector<vector<int>> levelOrder(Node* root) 
    {
        vector<vector<int>> ret;
        if(root == nullptr)
            return ret;
        queue<Node*> qe;
        qe.push(root);
        while(!qe.empty())
        {
            int size = qe.size();
            vector<int> tmp;
            for(int i = 0; i < size; i++)
            {
                // 取队列头节点
                Node* front = qe.front();
                qe.pop();
                // 把值入到数组中
                tmp.push_back(front->val);
                // 如果有孩子，就把孩子入到队列中
                for(int j = 0; j < (front->children).size(); j++)
                    qe.push((front->children)[j]);
            }
            ret.push_back(tmp);
        }
        return ret;
    }
};

二叉树的锯齿形层序遍历

这里提供一种双端队列的做法，也可以在合适的层数逆序

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode() : val(0), left(nullptr), right(nullptr) {}
 *     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
 *     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
 * };
 */
class Solution 
{
public:
    vector<vector<int>> zigzagLevelOrder(TreeNode* root) 
    {
        vector<vector<int>> res;
        if(root == nullptr)
            return res;
        bool status = true;
        queue<TreeNode*> qe;
        qe.push(root);
        while(!qe.empty())
        {
            int size = qe.size();
            deque<int> v;
            for(int i = 0; i < size; i++)
            {
                TreeNode* front = qe.front();
                qe.pop();
                if(status)
                    v.push_back(front->val);
                else
                    v.push_front(front->val);
                if(front->left) 
                    qe.push(front->left);
                if(front->right) 
                    qe.push(front->right);
            }
            res.push_back(vector<int>(v.begin(), v.end()));
            status = !status;
        }
        return res;
    }
};

二叉树的最大宽度

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode() : val(0), left(nullptr), right(nullptr) {}
 *     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
 *     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
 * };
 */
class Solution 
{
public:
    int widthOfBinaryTree(TreeNode* root) 
    {
        // 用数组来模拟队列，有助于最后计算，这里没用
        queue<pair<TreeNode*, unsigned int>> v;
        v.push(make_pair(root, 1));
        unsigned int lenth = 0;
        while(!v.empty())
        {
            // 计算一下这中间长度的差
            lenth = max(lenth, v.back().second - v.front().second + 1);
            int size = v.size();
            for(int i = 0; i < size; i++)
            {
                // 取头
                auto front = v.front();
                v.pop();
                // 如果有左或者有右节点，就进去
                if(front.first->left) 
                    v.push(make_pair(front.first->left, (front.second) * 2));
                if(front.first->right) 
                    v.push(make_pair(front.first->right, (front.second) * 2 + 1));
            }
        }
        return lenth;
    }
};

BFS和FLoodFill相结合

图像渲染

class Solution 
{
    int dx[4] = {1, -1, 0, 0};
    int dy[4] = {0, 0, 1, -1};
public:
    vector<vector<int>> floodFill(vector<vector<int>>& image, int sr, int sc, int color) 
    {
        int oldcolor = image[sr][sc];
        int newcolor = color;
        if(oldcolor == newcolor)
            return image;
        queue<pair<int, int>> q;
        q.push({sr, sc});
        while(!q.empty())
        {
            auto [a, b] = q.front();
            q.pop();
            image[a][b] = newcolor;
            for(int k = 0; k < 4; k++)
            {
                int x = dx[k] + a, y = dy[k] + b;
                if(x >= 0 && x < image.size() && y >=0 && y < image[0].size() && image[x][y] == oldcolor)
                    q.push({x, y});
            }
        }
        return image;
    }
};

岛屿数量

class Solution
{
    int res = 0;
    int dx[4] = { 1, -1, 0, 0 };
    int dy[4] = { 0, 0, 1, -1 };
public:
    int numIslands(vector<vector<char>>& grid)
    {
        vector<vector<bool>> check;
        check.resize(grid.size(), vector<bool>(grid[0].size(), false));
        queue<pair<int, int>> q;
        for (int i = 0; i < grid.size(); i++)
        {
            for (int j = 0; j < grid[0].size(); j++)
            {
                if (grid[i][j] == '1' && check[i][j] == false)
                {
                    check[i][j] = true;
                    q.push({ i, j });
                    while (!q.empty())
                    {
                        auto [a, b] = q.front();
                        q.pop();
                        for (int k = 0; k < 4; k++)
                        {
                            int x = dx[k] + a, y = dy[k] + b;
                            if (x >= 0 && x < grid.size() && y >= 0 && y < grid[0].size() && grid[x][y] == '1' && check[x][y] == false)
                            {
                                check[x][y] = true;
                                q.push({ x, y });
                            }
                        }
                    }
                    res++;
                }
            }
        }
        return res;
    }
};

岛屿的最大面积

class Solution 
{
public:
    int maxAreaOfIsland(vector<vector<int>>& grid) 
    {
        int res = 0, maxsize = 0, dx[4] = {1, -1, 0, 0}, dy[4] = {0, 0, 1, -1};
        vector<vector<bool>> check(grid.size(), vector<bool>(grid[0].size(), false));
        queue<pair<int, int>> q;
        for(int i = 0; i < grid.size(); i++)
        {
            for(int j = 0; j < grid[0].size(); j++)
            {
                if(check[i][j] == false && grid[i][j] == 1)
                {
                    check[i][j] = true;
                    q.push({i, j});
                    res++;
                    while(!q.empty())
                    {
                        auto [a, b] = q.front();
                        q.pop();
                        for(int k = 0; k < 4; k++)
                        {
                            int x = dx[k] + a, y = dy[k] + b;
                            if(x >= 0 && x < grid.size() && y >= 0 && y < grid[0].size() && grid[x][y] == 1 && check[x][y] == false)
                            {
                                check[x][y] = true;
                                q.push({x, y});
                                res++;
                            }
                        }
                    }
                    maxsize = max(res, maxsize);
                    res = 0;
                }
            }
        }
        return maxsize;
    }
};